# Fractions Calculator

The calculator will find (with steps shown) the sum, difference, product, and result of the division of fractions or mixed numbers. It will also convert the fraction into a decimal number and into an improper fraction (if possible).

Enter fractions or

First fraction:

Second fraction:

The second fraction is needed for addition, subtraction, multiplication, division; but not for converting to decimal.
If you don't need a mixed number, leave the left cell empty.
If you need a negative fraction, write the minus sign in the left cell.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

## Solution

Your input: find the sum, difference, and product of two fractions, the result of the division; convert them into decimal.

The fractions are: $2\frac{3}{7}$, $\frac{5}{9}$

Convert $2\frac{3}{7}$ into an improper fraction.

Rewrite $2$ as $\frac{14}{7}$

Add the fractions: $2\frac{3}{7}=\frac{14}{7}+\frac{3}{7}=\frac{17}{7}$ (we just add the numerators, since the denominators are equal).

So, $2\frac{3}{7}=\frac{17}{7}$

Multiply the numerator and the denominator of the first fraction by $9$: $\frac{17}{7}=\frac{153}{63}$

Multiply the numerator and the denominator of the second fraction by $7$: $\frac{5}{9}=\frac{35}{63}$

Add the fractions: $\frac{153}{63}+\frac{35}{63}=\frac{188}{63}$ (we just add the numerators, since the denominators are equal).

Convert into a mixed number.

Rewrite $188$ as $2 \cdot 63+62$: $\frac{188}{63}=\frac{2 \cdot 63+62}{63}=2\frac{62}{63}$

So, $\frac{188}{63}=2\frac{62}{63}$

## Fractions subtraction

Multiply the numerator and the denominator of the first fraction by $9$: $\frac{17}{7}=\frac{153}{63}$

Multiple the numerator and the denominator of the second fraction by $7$: $\frac{5}{9}=\frac{35}{63}$

Subtract fractions: $\frac{153}{63}-\frac{35}{63}=\frac{118}{63}$ (we just subtract the numerators, since the denominators are equal).

Convert into a mixed number.

Rewrite $118$ as $1 \cdot 63+55$: $\frac{118}{63}=\frac{1 \cdot 63+55}{63}=1\frac{55}{63}$

So, $\frac{118}{63}=1\frac{55}{63}$

## Fractions multiplication

Multiple the numerators and denominators: $\frac{17}{7} \cdot \frac{5}{9}=\frac{85}{63}$

Convert into a mixed number.

Rewrite $85$ as $1 \cdot 63+22$: $\frac{85}{63}=\frac{1 \cdot 63+22}{63}=1\frac{22}{63}$

So, $\frac{85}{63}=1\frac{22}{63}$

## Fractions division

Multiple the first fraction by inverted second fraction: $\frac{17}{7} \div \frac{5}{9}=\frac{17}{7} \cdot \frac{9}{5}=\frac{153}{35}$

Convert into a mixed number.

Rewrite $153$ as $4 \cdot 35+13$: $\frac{153}{35}=\frac{4 \cdot 35+13}{35}=4\frac{13}{35}$

So, $\frac{153}{35}=4\frac{13}{35}$

## Decimal representation

The decimal representation of $\frac{17}{7}$ is $2.42857142857143$

The decimal representation of $\frac{5}{9}$ is $0.555555555555556$

$2\frac{3}{7}+ \left( \frac{5}{9} \right)=\frac{188}{63}=2\frac{62}{63}$
$2\frac{3}{7}- \left( \frac{5}{9} \right)=\frac{118}{63}=1\frac{55}{63}$
$2\frac{3}{7} \cdot \left( \frac{5}{9} \right)=\frac{85}{63}=1\frac{22}{63}$
$2\frac{3}{7} \div \left( \frac{5}{9} \right)=\frac{153}{35}=4\frac{13}{35}$
The decimal representation of $2\frac{3}{7}$ is $2.42857142857143$
The decimal representation of $\frac{5}{9}$ is $0.555555555555556$